Answer:
A ticket for Petra's group is $8.50
Explanation:
Petra's Group
Each bought one ticket and spent $5.50 on snacks. There were five in the group (Petra and four friends). Total expenses:
5(x+5.50)
Valentina's Group
Each bought one ticket and spent $4.75 on snacks. There were four in the group (Valentina and three friends). Their tickets were 1.5 times the price of Petra's group, so 1.5x is the cost of each ticket. Total expenses:
4(1.5x+4.75)
We learn both spent the same amount, so set them equal to each other:
5(x+5.50) = 4(1.5x+4.75)
The student's mistake was in the number of people in each group. She had
4 in Petra's group (should be 5) and 3 in Valentina's group (should be 4)
Using the correct equation:
5(x+5.50) = 4(1.5x+4.75)
5x+27.50 = 6x+19.00
-x = -8.50
x = $8.50 Price of a ticket for Petra's group.
1.5x = $12.75 Price of a ticket for Valentino's group.
Check to see if both groups did indeed pay the same total amounts:
Tickets Snacks Total
Petra: (5*8.50) = 42.50 (5*5.50) = 27.50 $70.00
Valentino: (4*12.75) = 51.00 (4*4.75) = 19.00 $70.00